Resident permits and work visa

No, you can not. If you come from a country outside the EEA area you need a work permit and a residence permit to work in Iceland. Your employer applies for the work permit and you apply for the residence permit. You must be out of the country, when a first work/residence permit is issued.
If you’re married to an Icelandic citizen you do not need a work permit, but you must apply for a residence permit

EEA citizens do not need a work permit, but they need a residence permit. Citizens of the other Nordic countries (Finland, Sweden, Denmark, Norway and the Faroe Islands) neither need residence nor work permits.